## Time-reversal breaking in QCD _{4}, walls, and dualities in 2 + 1 dimensions

## Abstract

We study SU(N ) Quantum Chromodynamics (QCD) in 3+1 dimensions with N _{ƒ} degenerate fundamental quarks with mass m and a θ-parameter. For generic m and θ the theory has a single gapped vacuum. However, as θ is varied through θ = π for large m there is a first order transition. For N _{ƒ} = 1 the first order transition line ends at a point with a massless η' particle (for all N ) and for N _{ƒ} > 1 the first order transition ends at m = 0, where, depending on the value of N _{ƒ}, the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the _{4}d bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different 3d phases. These turn out to be the phases of the recently studied 3d Chern-Simons matter theories, thus relating the dynamics of QCD _{4} and QCD _{3}, and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless 4d theory has an SU(N _{ƒ}) sigma model, the domain wall theory at low (nonzero) mass supports a 3d massless CP ^{Nƒ-1}more »

- Authors:

- Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
- Weizmann Inst. of Science, Rehovot (Israel); Stony Brook Univ., NY (United States). Simons Center for Geometry and Physics
- Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

- Publication Date:

- Research Org.:
- Inst. for Advanced Study, Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1502470

- Grant/Contract Number:
- SC0009988

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Anomalies in Field and String Theories, Chern-Simons Theories, Duality in Gauge Field Theories, Spontaneous Symmetry Breaking

### Citation Formats

```
Gaiotto, Davide, Komargodski, Zohar, and Seiberg, Nathan. Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions. United States: N. p., 2018.
Web. doi:10.1007/jhep01(2018)110.
```

```
Gaiotto, Davide, Komargodski, Zohar, & Seiberg, Nathan. Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions. United States. doi:10.1007/jhep01(2018)110.
```

```
Gaiotto, Davide, Komargodski, Zohar, and Seiberg, Nathan. Tue .
"Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions". United States. doi:10.1007/jhep01(2018)110. https://www.osti.gov/servlets/purl/1502470.
```

```
@article{osti_1502470,
```

title = {Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions},

author = {Gaiotto, Davide and Komargodski, Zohar and Seiberg, Nathan},

abstractNote = {We study SU(N ) Quantum Chromodynamics (QCD) in 3+1 dimensions with Nƒ degenerate fundamental quarks with mass m and a θ-parameter. For generic m and θ the theory has a single gapped vacuum. However, as θ is varied through θ = π for large m there is a first order transition. For Nƒ = 1 the first order transition line ends at a point with a massless η' particle (for all N ) and for Nƒ > 1 the first order transition ends at m = 0, where, depending on the value of Nƒ, the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the 4d bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different 3d phases. These turn out to be the phases of the recently studied 3d Chern-Simons matter theories, thus relating the dynamics of QCD4 and QCD3, and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless 4d theory has an SU(Nƒ) sigma model, the domain wall theory at low (nonzero) mass supports a 3d massless CPNƒ-1 nonlinear σ-model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.},

doi = {10.1007/jhep01(2018)110},

journal = {Journal of High Energy Physics (Online)},

number = 1,

volume = 2018,

place = {United States},

year = {2018},

month = {1}

}

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